Msc Thesis Rf Janssen

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Master of Science Thesis

The influence of laminar-turbulenttransition on the performance of a

propellerA numerical and experimental investigation

R.F. Janssen

April 24, 2015

The influence of laminar-turbulenttransition on the performance of a

propellerA numerical and experimental investigation

Master of Science Thesis

For obtaining the degree of Master of Science in Aerospace Engineeringat Delft University of Technology

R.F. Janssen

April 24, 2015

Faculty of Aerospace Engineering Delft University of Technology

Delft University of Technology

Copyright Aerospace Engineering, Delft University of TechnologyAll rights reserved.

DELFT UNIVERSITY OF TECHNOLOGYDEPARTMENT OF AERODYNAMICS

The undersigned hereby certify that they have read and recommend to the Faculty ofAerospace Engineering for acceptance the thesis entitled The influence of laminar-turbulent transition on the performance of a propeller by R.F. Janssen in ful-fillment of the requirements for the degree of Master of Science.

Dated: April 24, 2015

Supervisors:prof. dr. ir. L.L.M. Veldhuis

prof. Dr.-Ing. G. Eitelberg

Dipl.-Ing. C. Lenfers

dr. ir. B.W. van Oudheusden

Preface

This report is written as the final thesis as part of the Aerodynamics Master track for obtainingthe Masters Degree of Aerospace Engineer at Delft University of Technology.

This way I would like to thank my supervisors. I would like to thank Leo and Georg for theirsupervision and healthy discussions. They also taught me that the flow direction is alwaysfrom left to right and I should never forget that. I would also like to thank Carsten for hissupervision during my time at DLR and his continued support via email when I was back atthe university.

I would also like to thank the technical staff of the High Speel Lab, Nico van Beek, Henk-JanSiemer, Peter Duyndam and Frits Donker-Duyvis, without their support I could not haveperformed my wind tunnel tests.

Thanks to the rest of the people at the Transport Aircraft department of the DLR Insitute ofAerodynamics and Flow Technology. If I had questions I could alway ask them and everyonewould offer their help.

I would also like to thank all the people I met during my time at Delft University of Techno-logy. Especially the people from the aerodynamics basement, with whom I had some healthydiscussions, and who were always willing to lend a helping hand.

Finally I would like to thank my whole family for their support and understanding. Inparticular I would like to thank my parents, if it was not for their support I would have neverbeen able to finish this study. And I would also like to thank my sister, whom Ill miss nowshe moved to Australia.

Delft,April 24, 2015

Ruud Janssen

MSc Thesis R.F. Janssen

vi Preface

R.F. Janssen MSc Thesis

Summary

The influence of laminar-turbulent transition on a propeller blades performance is discussed inthis report. Numerical as well as experimental work has been performed. The computationalfluid dynamics (CFD) is performed using the German Aerospace Center (DLR) developedTAU code, as well as an existing propeller lifting-line code. The laminar-turbulent transitionis simulated using the Ret correlation based transition model, which is compared to theresults of the Spalart-Allmaras one-equation turbulence model. To validate the CFD data,experiments are performed in the Open Jet Facility of Delft University of Technology wherethe laminar-turbulent transition is measured using an infrared camera.

The Ret correlation based transition model showed strange behaviour for advance ratiosbelow 1. After investigation it was found that vortical structures were forming in the flownear the propeller blade. The results showed that at an advance ratio of 1.2, a separationbubble was formed on the aft part of the blade. At and advance ratio of 1.0, the separationregion moves toward the leading edge, and at the same time the vortical structures started toform on the aft part of the blade. Decreasing the advance ratio to 0.8, the separation regionmoves to the leading edge and it can be seen that the strenght of the vortical structuresbecome stronger. On the lower half of the blade the separation region is near to the leadingedge, while near the blade tip still laminar flow is present up to around half chord. For anadvance ratio of 0.65 a strong separation can be seen, and again the vortical structures areformed.

From the numerical results it was found that the difference in thrust coefficient between theturbulence model and transition model changed from around 1% at an advance ratio of 0.65 toabout 27% at an advance ratio of 1.2. The differences in power coefficient changed from 1% atan advance ratio of 0.65, to about 23% at an advance ratio of 1.2. The propeller efficiency didnot have these large changes, at an advance ratio of 1.2 the difference in propeller efficiencychange approximately 6%, while at an advance ratio of 0.8 the change was about 0.06%.The differences between the blade element momentum theory and two RANS simulationswas larger, 57% lower values of the thrust coefficient for the RANS simulations. Due tothe two-dimensional nature of the blade element moment theory it is concluded that the liftcoefficients are high compared to RANS.

Qualitative infrared measurements have been performed on the propeller in a wind tunnel,this was done because the location of laminar-turbulent transition was of interest. From this


viii Summary

it was found that for decreasing advance ratio, the separation line moves toward the leadingedge. While at an advance ratio of 0.8, leading edge transition could be seen on the middlepart of the blade. It was also checked what the influence of the Reynolds number was onthe propeller blade. If the Reynolds number is changed, the state of the boundary layer alsochanges.

It can be concluded that the influence of laminar-turbulent transition on a propeller bladesperformance can be determined to some degree. Comparing the RANS simulations with thequalitative infrared measurements, some agreement between the results can be seen. The mainseparation regions are predicted quite accurate using the correlation based model. Due tothe formation of vortical structures on the blade there is still some doubt about the accuracyresults of the simulations.


Contents

Preface v

Summary vii

Nomenclature xi

1 Introduction 1

1.1 Transition and Propellers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.1.1 Laminar-Turbulent Transition . . . . . . . . . . . . . . . . . . . . . . . . 4

1.1.2 Laminar-Turbulent Transition Research on Propellers . . . . . . . . . . . 6

1.2 Research Aim and Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.3 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2 Numerical Setup 13

2.1 Propeller Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2 Blade Element Momentum Theory . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.3 Reynolds-Averaged Navier-Stokes equations . . . . . . . . . . . . . . . . . . . . 17

3 Experimental Setup 25

3.1 Wind Tunnel Facility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2 Propeller Test Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26


x Contents

3.3 Infrared Thermography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.4 Infrared Thermography Post-Processing Techniques . . . . . . . . . . . . . . . . 30

4 Numerical Results 33

4.1 Results for the Blade Element Momentum Theory . . . . . . . . . . . . . . . . . 33

4.2 Results for the Reynolds-Averaged Navier-Stokes Equations . . . . . . . . . . . . 34

4.2.1 Turbulent Model Results . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.2.2 Transition Model Results . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.2.3 Comparison Results Turbulent model and Transition model . . . . . . . . 57

4.3 Comparison BEMT and both RANS models . . . . . . . . . . . . . . . . . . . . 66

5 Experimental Results 73

5.1 Integration Time Influence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

5.2 Advance Ratio Influence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

5.3 Reynolds Number Influence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

6 Comparison Numerical and Experimental results 81

7 Conclusions and Recommendations 85

7.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

7.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

Bibliography 89

A Additional Numerical Results 93

A.1 Cp values on propeller blade surface . . . . . . . . . . . . . . . . . . . . . . . . 94

A.2 Cp values slices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

A.3 Blade loading characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106


Nomenclature

Latin Symbolsclstall Lift coefficient increment to stall []c Chord [m]cd Drag coefficient []Cf Skin friction coefficient, Cf = 2U2 []Ch Stanton number, Ch =

qu(hhw) []

cl Lift gradient[

1rad

]cl Lift coefficient []cm Pitching moment coefficient []CP Power coefficient, CP = Pn2D4 []Cp Pressure coefficient []CT Thrust coefficient, CT = Tn2D4 []D Propeller diameter [m]DL Digital Level [J ]Eb Radiated power from black body

[Wm2

]fv1 Spalart-Allmaras function []G Gain []H Shape Factor []h Enthalpy

[Jkg

]IT Integration time [s]J Advance Ratio, J = UnD []x Distance [m]M Mach number []n Propeller rotational speed

[1s

]O Offset []P Power [kW ]p Pressure [Pa]Pr Prandtl number []


xii Nomenclature

R Propeller radius [m]r Radial coordinate [m]Re Reynolds number []Ret Transition onset momentum-thickness Reynolds number []Re Momentum-thickness Reynolds number []Rev Strain-rate Reynolds number []RPM Propeller RPM

[revmin

]S Absolute value of strain rate

[1s

]Sij Strain-rate tensor

[1s

]T Temperature [K]T Thrust [N ]U Velocity

[ms

]u Velocity in X-direction

[ms

]v Velocity in Y -direction

[ms

]y+ Non-dimensional wall distance []

Greek Symbols Angle of attack [o] Zero-lift angle of attack [o] Blade pitch angle [o] Intermittency [] Relative difference [%] Displacement thickness [m]99 99% Boundary layer thickness [m] Emissivity coefficient [] Efficiency, = J CTCP [] Momentum thickness [m] Wavelength [m]

Dynamics viscosity[kgms

]t Eddy viscosity

[kgms

]t Eddy viscosity [Pa s] Spalart-Allmaras variable [Pa s] Density

[kgm3

] Stefan-Boltzmann constant, 5.670 108 [/fracWm2T 4] Shear stress [Pa] Vorticity vector

[rads

]Subscripts0 Minimum0.7R 70% blade span


xiii

Freestreamc Correctedcr Criticalcrit Criticale ExternalLIT Long Integration Timemax Maximummin Minimums SurfaceSIT Short Integration TimeTrans Transition RANS simulationTurb Turbulent RANS simulationuc Uncorrectedw Wallx X-directiony Y -directionz Z-direction

AbbreviationsBEMT Blade Element Momentum TheoryBNF Burgernahes FlugzeugBPR Bad Pixel ReplacementCFD Computational Fluid DynamicsDLR German Aerospace CenterIR InfraredNETD Noise equivalent Temperature DifferenceNLR National Aerospace Laboratory of the NetherlandsNUC Non Uniformity CorrectionOJF Open Jet FacilityQESTOL Quiet-Efficient-Short-Take-Off-and-Landing AircraftRANS Reynolds-Averaged Navier-Stokes EquationsRotGISF Rotational-Flow Global Interferometry Skin FrictionRPM Rotations Per MinuteTDI Tech Development Inc.TS Tollmien-Schlichting


xiv Nomenclature


Chapter 1

Introduction

Air traffic is growing steadily over the last couple of decades, doubling every 15 years. It isexpected this trend will continue for the next years [1], this can be seen in figure 1.1a. Withthe increase in air traffic the demand for new aircraft will increase. It is expected that mostof these new aircraft will be of the category of single-aisle aircraft, this can be seen in figure1.1b.

This increase in aircraft can lead to serious airport congestion at the major airports around theworld. This could be solved by expanding the current airports, but this is not always possibledue to environmental or residential constraints. Because most of the aircraft deliveries fall inthe single-aisle category it should be possible to shift air traffic to smaller, already existing,airports.

These small airports often have shorter runways which can not handle the current generationof single-aisle aircraft. The runway length could be increased, but as with the larger airportsthis is not always possible. Another way to solve this is by designing a short take-off andlanding aircraft. In the German research project Burgernahes Flugzeug (BNF) the key tech-nologies for a new quiet-efficient-short-take-off-and-landing aircraft (QESTOL) are developed[2]. In the BNF project a QESTOL configuration is investigated using computational fluiddynamics (CFD) and wind tunnel experiments. The QESTOL aircraft is defined as a twin-engine single-aisle aircraft with a passenger capacity of 150, utilizing a gapless blown trailingedge flap high-lift system. To get the best performance of the high-lift system an advancedturboprop propulsion system is chosen.

Because of the importance of the interaction between the high-lift system and the turboproppropulsion system, it is important to get a detailed and correct analysis of the turboproppropulsion system. To get a detailed analysis of the turboprop propulsion system a CFDanalysis, using the Reynolds-averaged Navier-Stokes (RANS) equations, is done to simulatethe propeller. Using RANS to simulate the propeller usually assumes the whole flowfieldto be turbulent, but it is expected that the influence of laminar flow and laminar-turbulenttransition has a big influence on the performance of the turboprop propulsion system.


2 Introduction

(a) Worldwide annual air traffic

(b) New aircraft demand for the period 2013-2032

Figure 1.1: Annual air traffic and new aircraft demand as predicted by Airbus [1]

1.1 Transition and Propellers

A fluid is not frictionless and therefore at walls and other interfaces a no-slip condition ispresent. This means that the velocity of the fluid at the wall is equal to the velocity of thewall itself. At a stationary flat plate, this means that u and v are both zero at the wall whenlooking at a two-dimensional flow. This no-slip condition leads to the existence of a thinboundary layer [3], a region in the flow field where the velocity of the flow changes from theno-slip condition to the velocity of the flow outside the boundary layer. The main controllingparameter in viscous flows is the dimensionless Reynolds number, given in equation (1.1).

Re =UL

(1.1)

Boundary layers are subdivided in two types, laminar boundary layers and turbulent boundarylayers. Laminar boundary layers have a smooth profile, whereas turbulent boundary layersare fluctuating [4]. In figure 1.2 the friction coefficient can be seen for increasing Reynoldsnumber for a flat plate [5]. As can be seen there are two regions, first a laminar flow and nexta turbulent flow after a Reynolds number of around 5 105. It can be seen that the value ofthe friction coefficient increases when the flow changes from laminar to turbulent flow. Fromthis it can be seen that a laminar boundary layer is preferred over a turbulent one to minimizefriction losses.

The flat plate boundary layer has been studied extensively and much is known about this typeof boundary layer. Using the analysis by Karman one can derive the Karman type integralrelations. In figure 1.3 the flow past a flat plate is shown. The outer streamline is taken asthe position where the velocity has reached 99% of the external flow velocity. When the inlet,outlet, plate and outer streamline are taken as the control volume for the integral analysis,one arrives at the compressible integral relations given in equations (1.2), (1.3) and (1.4) [4].These equations can be very useful in analysing the properties of boundary layers. The valueof shows what the displacement effect of the boundary layer is, as shown in figure 1.3.Here it can be seen that the boundary layer in effect adds thickness to the body contour.The momentum thickness, , is related to the drag. H is called the shape factor and this isa value which is often used in boundary layer analysis [4].

= 99

0

(1 u

Ue

)dy (1.2)


1.1 Transition and Propellers 3

Figure 1.2: Friction coefficient for flat plate flow [5]

= 99

0

u

Ue

(1 u

Ue

)dy (1.3)

H =

(1.4)

Figure 1.3: Displacement effect of a boundary layer [6]

Pure laminar boundary layers are well understood nowadays. As well as pure turbulentboundary layers, even though the finest scales of turbulence are still part of thorough in-vestigation. The problem is in the connection of laminar and turbulent boundary layers, thelaminar-turbulent transition.


4 Introduction

1.1.1 Laminar-Turbulent Transition

Laminar-turbulent transition in flows normally arises from small instabilities in the flow [7].The way these instabilities grow depends on the initial conditions provided by the freestreamconditions [8].

Two-Dimensional flows

Transition in two-dimensional flows can be classified in three cases [9]. These three cases are

Natural transition. Natural transition is the laminar-turbulent transition occuring dueto small instabilities in the flow which grow and form two- dimensional Tollmien-Schlichting (TS) waves. These TS waves grow and form three-dimensional loop vorticeswith high fluctuations. After this the high fluctuations in the flow develop into turbu-lent spots which eventually develop into a fully turbulent flow. This process is shownin figure 1.4.

Bypass transition. When the freestream disturbances are very strong it is possible thatthe flow transitions to turbulent very quickly because of turbulent spots or subcriticalinstabilities. This kind of transition is then called bypass transition [10]. Main causesfor this kind of transition are roughness and high freestream turbulence levels [11].

Separated-flow transition. Transition due to laminar separation is called separationinduced transition. When a laminar boundary layer separates under the influence of apressure gradient it is possible a transition zone develops within the separation bubble[12]. This type of transition is shown in figure 1.5.

Figure 1.4: Idealized sketch oflaminar-turbulent transition on a flatplate [13]

Figure 1.5: Sketch of separated-flowtransition [13]



Three-Dimensional flows

In three-dimensional flows the behaviour is completely different compared to the correspond-ing two-dimensional flow. Most studies on three-dimensional boundary layers are directedtoward swept wing flows. In these swept wing flows, four instability types were found thatlead to transition: leading edge instability, streamwise instability, centrifugal instability andcrossflow instability. In figure 1.6 a sketch is shown with the instabilities working on a sweptwing.

Figure 1.6: Instabilities found onswept wing flow [14]

Figure 1.7: Boundary layer profilewith crossflow present [7]

Leading edge instability is connected to the basic instability of the attachment-line flowor to turbulent disturbances that propagate along the wing leading edge [15].

Streamwise instability is similar to the two-dimensional instability, where TS waves aredeveloped.

Centrifugal instability plays a role in concave surface regions on the swept wing. HereGortler vortices appear in the flow leading to transition [16].

Crossflow instability is linked to the in-plane curvature of the streamlines [14], whichcause centrifugal forces. Outside the boundary layer these centrifugal forces are balancedwith the pressure forces. But inside the boundary layer these centrifugal forces decreasewhen nearing the wall, leading to the crossflow component. This is shown in figure1.7. Because the crossflow component of the flow must tend to zero when nearing theboundary layer edge, an inflection point must be present. Inflection points in boundarylayers are a necessary and sufficient condition for instability [17], making crossflow aninflectional instability.

Most of the times in three-dimensional flow all of these instabilities interact with one otherand make it difficult to tell which instability is observed [14].


6 Introduction

1.1.2 Laminar-Turbulent Transition Research on Propellers

A propeller blade is a three-dimensional system which is rotating at high speed. This rotatingmotion increases the difficulty of the analysis of the laminar-turbulent transition. The firstwell known investigation of the effect of rotation on boundary layers was carried out by H.Himmelskamp [18]. Himmelskamp performed point-wise pressure measurements at differentradial sections on a rotating propeller blade. Figure 1.8 shows local lift coefficients at differentradial sections for different angles of attack. The results obtained by Himmelskamp show that

Figure 1.8: Local lift coefficients on a rotating propeller at various radial sections [18]

near the hub the local lift coefficient is increased, Himmelskamp concluded that this was dueto a delay of separation. The separation is delayed because of the additional accelarationforces which are present due to the Coriolis forces caused by the rotation of the blade. Theseadditional accelaration forces have the same effect as a favorable pressure gradient, thusdelaying the separation. Another effect could be due to the centrifugal forces felt by theparticles in the boundary layer, making the boundary layer thinner compared to the stationarytwo-dimensional case. Thin boundary layers are less sensitive to adverse pressure gradients,this means that due to the centrifugal forces transition to turbulence is delayed on a rotatingpropeller.

More recent is the research performed by Schulein et al [19]. Here a new measurementtechnique was proposed called rotational-flow global interferometry skin friction (RotGISF).The RotGISF technique was tested on a generic propeller model rotating at speeds up to 240[Hz] at freestream flow speeds between 30 and 70

[ms

]. RotGISF is an optical interferometry

which is based on the relation between the thinning of an oil film, applied on the blade surface,and the local shear stress. A schematic of the method is given in figure 1.9.

After processing, the interference images are obtained, two examples are shown in figure 1.10.Figure 1.10a shows the propeller operating at a high advance ratio, while figure 1.10b showsthe propeller operating at a low advance ratio. It can be seen that the flow pattern changeswhen the advance ratio is changed. The change in flow topology is sketched in figure 1.11 for



Figure 1.9: Schematic RotGISF technique used by Schulein et al [19]

(a)

(b)

Figure 1.10: Interference images after image processing, (a) J = 1.15 and (b) J = 0.81 [19]


8 Introduction

advance ratios between 0.50 and 1.20.

Figure 1.11a shows the flow topology for J = 0.50. It can be seen that near the hub the flowis laminar and a separation bubble is occuring near the trailing edge of the blade. Beyond thecritical radius, rcr, a leading edge separation bubble is starting to form. This leading edgeseparation bubble leads to a sudden transition to turbulent flow. At the outer part of theblade a large three- dimensional conical vortex is observed. It is thought this conical vortexis closely related to the delta wing vortices occuring at high angles of attack, because of thehigh leading edge sweep angle.

At an advance ratio of J = 0.80 it can be seen that the flow topology has changed, seefigure 1.11b. The critical radius is moving to the outer part of the propeller blade, while noconical separation vortex can be seen. Below the critical radius the flow is laminar and nearthe trailing edge a separation bubble is occuring. At J = 1.00 a large part of the blade islaminar, with a separation bubble at the trailing edge, this can be seen in figure 1.11c. Aleading edge separation bubble can only be seen at the tip of the blade, rcrR 0.8. Finallyit can be seen in figure 1.11d that at high advance ratios the flow is fully laminar, where aseparation bubble forms over the trailing edge of the blade.

The results from Schulein et al show some agreement with the work of Kuiper, who did anoptical investigation on a ship propeller [20]. Figure 1.12 shows an overview of the boundarylayer regimes found on the ship propeller blade. It can be seen that at the tip of the propeller,line AB, a short laminar separation bubble was observed near the leading edge. This shortseparation bubble makes the boundary layer turbulent over the rest of the blade chord. LineBC defines the critical radius, and Kuiper found it was strongly dependant on the propellerloading. Below the critical radius it was found that a transition region was formed, givenby line CD. Very close to the hub it was found that the flow was laminar and a laminarseparation bubble was formed, this is due to a low sectional Reynolds number combined witha thick propeller section.



(a) J = 0.50

(b) J = 0.80 (c) J = 1.00 (d) J = 1.20

Figure 1.11: Sketch of the flow topology over the suction side of the propeller blade at differentadvance ratios [19]


10 Introduction

Figure 1.12: Sketch of the flow topology on a ship propeller blade [20]


1.2 Research Aim and Objectives 11

1.2 Research Aim and Objectives

This section describes the proposed thesis question and objectives. The goal of the researchcan be reached by answering the main question and its sub-questions.

First the main research question:

Can the influence of laminar-turbulent transition on a propeller blades perform-ance be determined through the use of CFD and wind tunnel experiments?

To be able to answer the main question a couple of sub-questions should be answered first.These sub-questions are formulated as follows:

Is it possible to use current CFD models to calculate accurately the position of thelaminar-turbulent transition?

Is it possible to measure the laminar-turbulent transition using infrared thermography?

Do the results from the CFD simulations agree with the results from the wind tunnelexperiment?

Does laminar-turbulent transition influence the performance of a propeller?

From the main question and sub-questions the main objective of the thesis can be defined as:

Determine the influence of the laminar-turbulent transition on the performance ofa propeller, by means of CFD simulations and wind tunnel experiments.

1.3 Thesis Outline

This report consists of seven chapters. This first chapter is an introduction to work tobe presented. Chapter 2 will explain the numerical setup, here the propeller model to beinvestigated will be described as well as the computational techniques which will be usedfor the analysis. To be able to validate the results obtained by computations, chapter 3will give a description of the experimental setup as well as the post-processing techniqueswhich will be used. Having finished describing the experimental setup, chapter 4 will presentthe numerical results. Following the numerical results, chapter 5 will present the obtainedexperimental results. Having both numerical and experimental results, chapter 6 will comparethe numerical and experimental results. Finally, chapter 7 will present the conclusions drawnfrom this work together with recommendations for future research.


12 Introduction


Chapter 2

Numerical Setup

This chapter describes the numerical methods which are used to analyse the isolated pro-peller. First the XPROP propeller will be shown in section 2.1. Section 2.2 will explainthe Blade Element Moment Theory, with a short description about MSES and XROTOR.Finally, section 2.3 the Reynolds-Averaged Navier-Stokes equations will be elaborated upon,together with the computational grid and the used turbulence models.

2.1 Propeller Model

The propeller which is used to perform the simulations and experiments is the Delft Univer-sity of Technology XPROP propeller. Figure 2.1 shows the wind tunnel model of the XPROPpropeller and figure 2.2 shows the XPROP model used in the CFD simulations. When com-paring the two models, it can be seen that the connection between the hub and the propellerblade is not modelled correctly. This is due to missing information about the hub-propellerconnection in the XPROP documentation.

In the CFD model, a right handed coordinate system is used. As can be seen in figure 2.2, theY -axis is defined in positive up direction, the Z-axis is defined to the right as positive, whichmeans the X-axis is pointing away from the reader. The origin of the coordinate system isdefined at r = 0 [m] at the location where the spinner starts.

The XPROP propeller is a six-bladed propeller which has a diameter of 0.4064 [m]. Thehub of the propeller is 0.0884 [m] in diameter. The blade pitch angle of the propeller can beadjusted, and it was chosen to set the blade pitch angle at 30[o] at 70% of the blade span.An overview of the XPROP propeller characteristics is given in Table 2.1.


14 Numerical Setup

Figure 2.1: Front view wind tunnelmodel of the XPROP propeller

Figure 2.2: Front view CFD model ofthe XPROP propeller

Table 2.1: XPROP propeller characteristics

Number of blades 6Propeller diameter 0.4064 [m]

Hub diameter 0.0884 [m]Blade pitch angle at rR = 0.7 30 [

o]


2.2 Blade Element Momentum Theory 15

2.2 Blade Element Momentum Theory

A classical approach in the design and analysis of propeller blades is the Blade ElementMomentum Theory (BEMT). BEMT is a combination of the blade element theory and themomentum theory for propellers. The BEMT used in this work uses a combination of MSESand XROTOR. MSES is used to obtain the blade section characteristics, while XROTORcalculates the propeller performance.

MSES

To obtain the XPROP airfoil data the program MSES, written by M. Drela, is used. MSESis based on the steady Euler equations which are discretised using a finite volume method.To account for boundary layers, a two-equation integral formulation with lagged-dissipationclosure model is used. The displacement thickness is used to couple the viscous and inviscidregions of the flow [21].

The inviscid flow is resolved using the steady Euler equations [22]. These Euler equations aresolved by a full Newton method on an conservatively discretised intrinsic streamline grid.

The boundary layer is calculated using a two-equation integral formulation based on dissipa-tion closure which is valid for both laminar and turbulent flows. To account for transition theeN method developed by van Ingen [23] and Smith and Gamberoni [24] is utilised. The eN

method assumes transition when the most unstable Tollmien-Schlichting wave in the bound-ary layer has grown by a factor of eN , where often N is chosen as 9.

Coupling the discrete inviscid Euler equations together with the discrete boundary layerequations, a system of nonlinear equations is obtained. To solve this system of nonlinearequations a Newton solution procedure is used [22]. Because the resulting Newton matrix isvery sparse and structured it can be solved very fast using a direct Gaussian block-eliminationmethod. Figure 2.3 shows a simplified diagram of the solution procedure MSES uses.

Panel solutionInitial surface

gridGrid

smoothingInitial solution

Circulation converged?

clcdcm

TF

Blade geometryFreestream conditions

Figure 2.3: Simplified diagram of solution procedure MSES

The input of a simulation consists of the blade section geometry, freestream conditions andsimulation parameters [21]. Using these inputs, first a panel solution is obtained. This panel


16 Numerical Setup

solution divides up the domain in blocks, giving the skeleton to generate the grid. After thepanel solution is obtained an initial surface grid is constructed, which distributes the surfacenodes over the blade geometry. The obtained surface grid is smoothed using an elliptic gridsmoother to remove kinks and overlaps, and makes the grid streamlines correspond to thestreamlines of the panel solution. Using the obtained grid an initial solution is calculated.After this, the Euler equations and boundary layer equations are solved using a Newtoniteration method. After the solution is converged the lift, drag and moment coefficients aregiven as outputs which are used as input for the XROTOR program.

XROTOR

The XROTOR program is written by the same person as the MSES program, M. Drela.XROTOR is released under the GNU General Public License in 2011. XROTOR utilizesthe classical propeller lifting-line theory, which allows for the specification of lift and dragproperties, without giving geometrical data. To take compressibility into account for higherMach number flows, Prandtl-Glauert correction is applied.

XROTOR uses an iterative solution procedure, which can be seen in figure 2.4. The initial

Compute initial

circulationSet circulation

Compute induced

velocities

Compute section

values

Compute section cl and

cd values

Compute circulation

Circulation converged?

Compute updated

circulation

Compute CT, CP and

TF

Figure 2.4: Simplified diagram of solution procedure XROTOR. Reproduced from [25]

circulation is calculated assuming no induced effects are present. Knowing the initial circu-lation a Newton iteration method is used to obtain a converged solution for the circulation.When the circulation has converged the values for the thrust coefficient, torque coefficientand efficiency are calculated.

For each blade section the following parameters have to be provided:

Maximum lift coefficient, clmax Minimum lift coefficient, clmin Zero-lift angle, 0 Lift gradient, cl Lift gradient after stall,

[cl

stall

Lift increment to stall, clstall


2.3 Reynolds-Averaged Navier-Stokes equations 17

Minimum drag, cd0 Lift coefficient at minimum drag coefficient, c

cd=cd0l

Gradient of drag coefficient with respect to lift coefficient squared, cdc2l

Critical Mach number, Mcrit

These parameters are obtained from the results of the airfoil calculations performed by MSES.The obtained lift and drag curves for each blade section are fitted using multi-variable optim-izations using a Matlab routine provided by T. Sinnige which uses a Nelder-Mead optimizationmethod [25].

2.3 Reynolds-Averaged Navier-Stokes equations

For the Reynolds-Averaged Navier-Stokes (RANS) simulations of the XPROP propeller theGerman Aerospace Center (DLR) developed TAU code is used. The development of the TAUcode was started in the German CFD project MEGAFLOW [26], which was a collaborationbetween DLR, German universities and the German aircraft industry.

The TAU code is an unstructured CFD solver which can solve the unsteady RANS equations.It is well suited for mixed-element meshes consisting of tetrahedron, prisms, hexahedra andpyramids [27].

The XPROP propeller will be evaluated using a fully turbulent model and a model includ-ing laminar-turbulent transition. Table 2.2 gives the operating points which are simulatedusing both the fully turbulent and transition model, where n is the rotation frequency of thepropeller. For the spatial discretisation a central finite volume approach is chosen. The timediscretisation is done using a Runge-Kutta scheme. In the past these settings have proven togive good results for propeller simulations using the DLR TAU code [28] [29].

Table 2.2: Propeller operating points for the CFD simulations, 0.7R = 30 [o]

J [-] v[ms

]n[

1s

]0.3 26 213.250.5 26 127.950.65 26 98.450.8 26 79.971.0 26 63.981.2 26 53.31

Computational Grid

The computational grids for the XPROP propeller are generated using the commercial soft-ware Centaur, developed by CentaurSoft [30]. As stated before the mesh can consist of


18 Numerical Setup

mixed-elements. Near the wall prism elements will be used, while the remaining domain willconsist of tetrahedral elements. The grid is constructed using best practice guidelines andpersonal experience obtained working on the BNF project [28].

The mesh size can be reduced by simulating only one propeller blade and utilising periodicboundary conditions, this is shown in figure 2.5 where the simulated part is highlighted inblack and red. The use of periodic boundary conditions puts a few restictions on flows whichcan be investigated, namely only flows where the flow direction is parallel to the rotation axis.The periodic boundary conditions would also give rise to an unphysical rotating boundarylayer over the spinner and nacelle surfaces, so the spinner and nacelle surfaces are set asinviscid walls, highlighted in black in figure 2.5. From a previous study [28] it was also foundthat a small error in surface mesh discretisation led to a region of separated flow on the aftpart of the nacelle. To overcome this problem it was opted to extend the nacelle to the end ofthe domain. To further simplify the modeling, the whole domain is rotating with the propellerblade. Because of this simplification no sliding mesh or Chimera approach is needed, furtherreducing the computational costs.

The surface of the propeller, the spinner and the nacelle are discretised using triangularelements. The surface grid of the propeller blade is shown in figure 2.6. As the blade is thin,additional refinement is done at the leading edge, this is shown in figure 2.7.

To ensure the boundaries have no influence on the final solution, the domain extends from10 [m] upstream of the propeller blade, to 10 [m] downstream of the blade and the domainhas a height of 10 [m]. The 10 [m] was chosen because it was around 50 times the propellerradius. To resolve the flow more accurate near the blade the volume mesh is fine nearthe blade surface, while it is coarse far away form the blade. This is allowed, as far awayfrom the blade the flow is almost uniform and no large variable changes are present. A finerefinement region of the volume mesh, having a radius of 1.2 times the propeller radius, ischosen to start at an X position where the spinner starts, and this region extends to about6 propeller diameters downstream. To avoid sudden changes in tetrahedral size, regions ofgradual refinement are defined around the fine refinement area. The complete volume meshis constructed of approximately 41 million elements, 13 million prism elements and 28 milliontetrahedral elements. The volume mesh for the complete domain can be seen in figure 2.8,where a slice at Z = 0 is shown. The regions of coarse and finer elements can be seen. Tobetter show the volume mesh near the propeller blade, figure 2.9 shows the volume meshzoomed in more around the blade.

Finally in figure 2.10 the blade tip is shown where also the distinction can be made betweenthe prism elements and the tetrahedral elements. The height of the first cell over the bladesurface is constructed to be y+ = 1. This is needed for resolving the boundary layer in thesimulations.



Figure 2.5: Simulated part of the XPROP propeller, highlighted in black is the spinner andnacelle, and in red the propeller blade

Figure 2.6: Surface grid propellerblade

Figure 2.7: Zoom of top corner sur-face grid propeller blade


20 Numerical Setup

Figure 2.8: Volume mesh of the complete domain, slice at Z = 0

Figure 2.9: Volume mesh, slice at Z = 0



Figure 2.10: Zoom of volume grid at blade tip, slice at Z = 0

Turbulent model

The Reynolds averaging of the Navier-Stokes equations leads to the RANS equations. Next tothe unknown pressure and three velocity components, Reynolds averaging also introduces sixunknowns, the Reynolds stress components uiuj [31]. This means there are ten unknowns,while there are only four equations: mass conservation and the three momentum equations.This means that the system of equations is not closed, and to close the system additionalequations are needed which model the Reynolds stress components. These Reynolds stressmodels can be divided in multiple categories:

Algebraic (zero-equation) models; One-equation models; Two-equation models; Second-order closure models (Reynolds stress equation models).

Here the zero-, one- and two-equation models use the Boussinesq approximation to modelthe Reynolds stresses. The Reynolds stress equation (RSE) models use the exact differentialequation for the Reynolds stress tensor, which makes them computationally more intensive.

For this thesis it was chosen to use the Spalart-Allmaras one-equation model [32] as it hasshown good results compared to experiments, see Sturmer et al [29].

The Spalart-Allmaras model is written in terms of the eddy viscosity t, equation (2.1), withthe Reynolds stresses given by uiuj = 2tSij [32].

t = fv1 (2.1)


22 Numerical Setup

Here is the working variable, which is obtained solving a transport equation, and fv1 is afunction. If the reader is interested in the full description of the Spalart-Allmaras model, thereader is referred to the paper written by P. Spalart and S. Allmaras [32].

Transition Prediction model

The prediction of laminar-turbulent transition in CFD applications can be accomplished usingdifferent methods. First there are the weak coupling methods, which calculate the meanflow field, followed by a boundary layer calculation [33]. The second method is using so-called stability techniques such as the eN -method developed by van Ingen [23] and Smithand Gamberoni [24]. Finally there are the correlation based techniques, one example is themethod developed by Langtry and Menter [34].

Here it is chosen to use the Ret correlation based transition model of Langtry andMenter as it has shown promising results in the simulation of turbomachinery [35] and windturbines [36]. The weak coupling methods and stability techniques also have difficulties withcomplex three dimensional flows, as is the case with the flow around a propeller blade. Thebig advantage of the correlation based transition model is that it uses only local variableswhich makes it ideal for implementation in a parallel CFD solver. In the DLR TAU code the Ret correlation based transition model is coupled with the SST k turbulence modelas was suggested by Langtry and Menter [34].

The model uses the strain-rate Reynolds number to link the transition onset Reynolds numberfrom an empirical correlation and local boundary layer quantities. The equation for the strain-rate Reynolds number is given in equation (2.2).

Rev =y2

uy = y2 S (2.2)

From equation (2.2) it can be seen that Rev is a local property as it only depends on thedensity , the wall distance y, viscosity and the shear strain rate S. The strain-rate Reynoldsnumber is scaled to have a maximum value of one inside the boundary layer. From this itfollows that the maximum of the strain-rate Reynolds number profile is proportional to themomentum-thickness Reynolds number, given in equation (2.3). The value of 2.193 is chosensuch that for a Blasius profile max

(2.193ReRev

)= 1.

Re =max (Rev)

2.193(2.3)

The link between the strain-rate Reynolds number and the empirical tranition correlationsis accomplished using two transport equations. One for the intermittency , which is usedto trigger the tranisition locally, given in equation (2.4). And one transport equation for thetransition onset momentum thickness Reynolds number, Ret, which is required to capture thenonlocal influence of the turbulence intensity, given in equation (2.7). This second transportequation connects the empirical transition correlations to the transition onset criteria in the



intermittency transport equation.

()t

+ (Uj)xj

= P E + xj

[(+

tf

)

xj

](2.4)

The value f in equation (2.4) is a constant. The transition sources in the intermittencytransport equation are given by P1, see equation (2.5). Flength is an empirical correlationwhich controls the transition region length. S is the strain-rate magnitude. Fonset is acorrelation which controls the transition onset location. It should be noted that both Flengthand Fonset are dimensionless functions, while ca1 and ce1 are constants.

P1 = Flengthca1S [Fonset]0.5 (1 ce1) (2.5)

The E is given as the destruction/relaminarization source and is given in equation (2.6).Again ca2 and ce2 are constants, while is the vorticity magnitude. Fturb is a function whichused to disable the destruction/relaminarization source outside of a laminar boundary layeror in the viscous sublayer.

E = ca2Fturb (ce2 1) (2.6)

To transform a non-local correlation for Ret into a local form, the tranport equation for thetransition momentum thickness is introduced, see equation (2.7).

(Ret

)t

+(UjRet

)xj

= Pt +

xj

[t (+ t)

Retxj

](2.7)

Here Pt is the source term which forces the transported scalar Ret to match the local valuesof the empirical correlations for Ret. The equation for Pt is given in equation (2.8). t isa model constant which controls the diffusion coefficient.

Pt = ct

t

(Ret Ret

)(1.0 Ft) (2.8)

In equation (2.8) ct is a constant which controls the magnitude of the source term. The timescale t is there for dimensional reasons and was determined on basis it had to scale with theconvective and diffusive terms in the transport equation. Ft is a blending function whichturns off the source term in the boundary layer and diffuses Ret in from the freestream.

For a detailed description of the model and how it was conceptualised the reader is referredto the dissertation of Langtry [37] and the paper by Langtry and Menter in which the fullmodel correlations have been published [34]. For the implementation in the DLR TAU codethe reader is referred to the paper by Grabe and Krumbein [38].


24 Numerical Setup


Chapter 3

Experimental Setup

This chapter explains the experimental setup used during the testing of the XPROP propellerin the wind tunnel to determine the transition location using infrared thermography. Section3.1 shows an overview of the wind tunnel. After this, section 3.2 gives an overview of thepropeller test setup. Subsequently, infrared thermography is elaborated upon in section 3.3.And finally in section 3.4 the post-processing techniques are explained.

3.1 Wind Tunnel Facility

The experiments were performed in the Open Jet Facility (OJF) of the Delft University ofTechnology. The OJF is a closed circuit open jet facility which has a maximum wind velocityof 30

[ms

], a schematic of the OJF is given in figure 3.1. The OJF features a test section

which is 6.0 [m] wide, 6.5 [m] high and 13.5 [m] long. The settling chamber is equippedwith a honeycomb flow rectifier and five fine-mesh screes to reduce the turbulence level of theflow and remove spatial velocity deviations. The velocity deviations are smaller than 0.5% inthe vertical plane at two meters from the outlet, and the OJF has a longitudinal turbulenceintensity level lower than 0.24%. Noise levels are reduced using perforated plates installed onmineral wood and sound absorbing foam which cover the entire tunnel. There are no specialmeasures taken to attanuate the fan noise [39].


26 Experimental Setup

Figure 3.1: Schematic of the Open Jet Facility with an wind turbine in the test section. Repro-duced from [39]

3.2 Propeller Test Setup

The experiments were conducted on the Delft University of Technology XPROP propeller.The chosen configuration was an isolated propeller to investigate the transition of laminar toturbulent flow on the blades. The test setup consists of several parts: the propeller itself, theair turbine motor, a heat source in the form of a 1 [kW ] power lamp, and finally the datameasurement hardware.

The XPROP propeller is driven using a Tech Development Inc. (TDI) 1999A air turbinemotor, which is supplied with air from the central air supply system of the Delft Universityof Technology High Speed Wind Tunnel Laboratory. The air turbine motor is designed todeliver 73 [kW ] at 22500 [RPM ] with a drive air total pressure of 34.47 [Bar] and a drive totalair temperature of 288.15 [K] [40]. A detailed description of the operation and installation ofthe air turbine is described in [41].

The temperature on the propeller blade surface was measured using an infrared camera, aswill be explained in more detail in section 3.3. To measure the temperature on the surfaceof a rotating propeller blade, phase locking is needed. This is done by supplying the infraredcamera with a trigger signal coming from the air turbine motor. This signal from the airturbine motor is generated by two magnetic pickups, which produce one pulse per revolution.The signal coming from the air turbine motor cannot be directly connected to the infraredcamera, a Stanford Research Systems DG535 Digital Delay/ Pulse Generator was used, asshown in Figure 3.2. The DG535 can measure external signals and give out precisely controlledpulses. These pulses can be used to trigger the infrared camera.

A schematic of the test set-up is shown in figure 3.3. The propeller test setup, consisting of


3.2 Propeller Test Setup 27

Figure 3.2: Stanford Research Systems DG535 Digital Delay/ Pulse Generator. Reproducedfrom [42]

the XPROP propeller, TDI 1999A air turbine motor, infrared camera and a 1 [kW ] lamp,can be seen in Figures 3.4 and 3.5. Figure 3.4 shows a side view of the test setup, and Figure3.5 shows a view of the propeller, lamp and infrared camera.

Figure 3.3: Schematic of the experimental test set-up



Figure 3.4: Side view of the wind tun-nel setup

Figure 3.5: View of the experimentalsetup

3.3 Infrared Thermography

In aerodynamics it can be useful to know the temperature distribution over a body. Especiallythe heat flux at the wall is of interest, as this can be related to the skin friction through theReynolds analogy, given in equation (3.1). Here, Cf is the friction coefficient, Ch the Stantonnumber and Pr the Prandtl number [4].

CfCh

= 2Pr23 (3.1)

Using the characteristic that laminar boundary layers have lower skin friction than turbulentboundary layers, using infrared thermography one can determine the state of the boundarylayer by looking at the temperature. Regions of high temperature on the propeller bladeindicate low heat flux and thus low skin friction, which would suggest the flow is laminarin those regions. Regions of low temperature on the other hand indicate a high heat flux,meaning high skin friction and thus a region of turbulent flow. During the measurements thepropeller blade will be heated using a heat source in the form of a high power lamp.

When an object has a temperature above absolute zero, it radiates electromagnetic radiation,which is linked to the temperature of the objects surface. For a black body, the wavelengthat which maximum radiation is emitted is given by Wiens displacement law, equation (3.2)


3.3 Infrared Thermography 29

[43].

maxTs = 2.898 103 [m K] (3.2)

For a body at 300 [K] this means max is around 10 [m]. The total power radiated from ablack body can be given by the Stefan-Boltzmann equation, which is the maximum radiatedpower possible at a certain temperature. For real bodies the Stefan-Boltzmann equation ismultiplied by , the spectral emissivity coefficient, which is 1 for a black body.

Eb = T 4 (3.3)

Here is the Stefan-Boltzmann constant, 5.670 108 [ Wm2K4

], and T is the surface temper-

ature.

The camera used during the experiments was the CEDIP Titanium 530L, as is shown inFigure 3.6. The camera uses a Focal Plane Array (FPA) sensor, consisting of 320 x 256detectors. These are Mercury Cadmium Telluride quantum detectors, which have a spectralresponse in the range of 7.7 [m] to 9.3 [m]. At full resolution, the maximum frame rate is250 [Hz]. The full specifications of the camera are given in Table 3.1. Here the abbrevationNETD stands for Noise Equivalent Temperature Difference, which is the smallest variationin detectable temperature.

Figure 3.6: CEDIP Titanium 530L camera. Reproduced from [44]

Table 3.1: CEDIP Titanium 530L specifications. Reproduced from [44].

Detector Material Mercury Cadmium TellurideSpectral Response 7.7 - 9.3 [m]

Frame Rate 250 [Hz]Pitch 30 x 30 [m]

NETD < 25 [mK] @ 25 [oC] & 350 [s] integration time without filterAperture F/2



The camera is connected to a computer, which controls the camera and is used to store theobtained images. The software which is used to control the camera is Altair [45]. The mainfunctions of Altair are:

Set integration time

Non Uniformity Correction (see section 3.4)

Camera trigger

Recording of the images

The integration time is the time a detector is exposed to the electromagnetic radiation, andas such determines how much radiation can be measured. The selection of integration timedetermines which temperature range can be measured.

The propeller is a rotating system, which makes it difficult to measure the temperaturewhen no phase locking is used. Using phase-locking, the camera makes a measurement whenthe blade is at the same position each rotation cycle. To accomplish this phase-locking thecamera is equiped with a trigger function.

The obtained infrared images are saved in the Cedip-PTW file format. To be able to viewthe images outside of the Altair software, a Matlab routine is available to read in the data asa matrix. After that operation is completed the data can be post-processed.

3.4 Infrared Thermography Post-Processing Techniques

The CEDIP Titanium 530L infrared camera utilizes an FPA sensor. This FPA sensor is madeup of multiple detectors, in the case of the CEDIP Titanium 530L 320 x 256 detectors, whereeach detector has its own characteristics. To correct for these differences in characteristics aNon Uniformity Correction (NUC) is applied. This NUC will introduce, for each detector, again value and an offset value. In this way all detector response curves will be brought in linewith the average curve for the entire sensor.

The NUC can be performed by the software provided by CEDIP itself. However, to obtainmore control over the resulting correction, a NUC is programmed in Matlab . The NUC whichis used is the two point time integration method. This method is chosen because it does notneed a black body at two different temperatures, but only one temperature is needed. Usingthe two integration times one can get a detector response curve. To get a good detectorresponse curve, multiple measurements need to be performed at each integration time.

A linear NUC is used, as from preliminary investigations it was found that a quadratic NUCdid not improve the results. The formula for the linear NUC is given in equation (3.4). HereDL stands for Digital Level, the output signal of the detectors in [J ]. The subscript c standsfor the corrected signal and uc is the uncorrected detector signal. The value G (i, j) is thegain of the detector and O (i, j) is the offset.

DLc (i, j) = G (i, j)DLuc (i, j) +O (i, j) (3.4)


3.4 Infrared Thermography Post-Processing Techniques 31

The values of G and O need to be determined for each detector on the sensor. Using twodifferent integration times, long and short, the values for G and O can be determined. In-troducting the term DLLIT for the detector signal for a long integration time, and DLSITfor the short integration time detector signal. As was said before, multiple measurements ateach integration time are needed to perform a correct NUC. The equations for the gain andoffset are given in (3.5) and (3.6). Here the values DLLIT and DLSIT are the mean DLof the complete sensor at a long integration time and short integration time respectively. Thevalues DLLIT (i, j) and DLSIT (i, j) are the mean values of the single detectors for the longand short integration time, respectively.

G (i, j) =DLLIT DLSIT

DLLIT (i, j)DLSIT (i, j)(3.5)

O (i, j) =DLLIT (i, j) DLLIT DLSIT (i, j) DLSIT

DLLIT (i, j)DLSIT (i, j)(3.6)

In figure 3.7 an example of obtained gain and offset values for a short integration time of 15[s] and long integration time of 25 [s] are shown. From the figures it can be seen that atsome places on the sensor the gain and offset have values which are completely out of rangein comparison with the rest of the sensor values. During the measurements these pixels willalso show up, and degrade the obtained image. A bad pixel is defined as a pixel where thegain value is 25% compared to the mean gain value of the complete sensor [46]. In figure3.8 it is shown where these pixels are located on the sensor. To correct for this a Bad PixelReplacement (BPR) is used.

The BPR uses weighted averaging of the surrounding pixel DLc values to obtain an interpol-ated value for the bad pixel. The weighting formula which was used is given in (3.7). Theinfluence of BPR can be seen in figure 3.9. In figure 3.9a the resulting infrared image can beseen without BPR, while in figure 3.9b the same infrared image is shown with BPR applied.It can be seen that the use of BPR greatly reduces the defects in the infrared image.

DLc,BPR =DLc,i+1,j +DLc,i1,j +DLc,i,j+1 +DLc,i,j1

1 + 1 + 1 + 1 + 12

+ 12

+ 12

+ 12

+

+12DLc,i+1,j+1 + 12DLc,i+1,j1 +

12DLc,i1,j+1 + 12DLc,i1,j1

1 + 1 + 1 + 1 + 12

+ 12

+ 12

+ 12

(3.7)



(a) Gain values (b) Offset values

Figure 3.7: Infrared sensor gain and offset values obtained from a short integration time of 15[s] and a long integration time of 25 [s]

Figure 3.8: Bad pixel locations onthe infrared camera sensor, indicatedby white dots

(a) No BPR (b) With BPR

Figure 3.9: Effect of BPR for an infrared image obtained at an integration time of 20 [s], usingthe gain and offset values from figure 3.7


Chapter 4

Numerical Results

This chapter will show the results obtained using the Blade Element Momentum Theory andthe Reynolds-Averaged Navier-Stokes simulations. First the results from the BEMT will bediscussed in section 4.1. After the BEMT results, the results from the RANS simulations willbe shown in section 4.2. Finally the results from the BEMT and RANS will be compared insection 4.3.

4.1 Results for the Blade Element Momentum Theory

In this section the results from the BEMT will be shown. BEMT is a relative simple technique,only the propeller performance and the forces acting on the propeller blades are given.

The performance of the XPROP propeller as computed with the BEMT is given in table 4.1,and is visualised in figure 4.1. From the table and the figure it can be seen that for decreasing

Table 4.1: Results obtained using BEMT

J [-] CT [-] CP [-] [-]1.40 0.0264 0.0985 0.37521.30 0.0782 0.1483 0.68551.20 0.1277 0.1949 0.78621.10 0.1747 0.2380 0.80741.00 0.2188 0.2771 0.78960.90 0.2599 0.3118 0.75020.80 0.2976 0.3412 0.69780.70 0.3316 0.3644 0.63700.65 0.3466 0.3729 0.60420.60 0.3606 0.3794 0.5703


34 Numerical Results

J [-]

C T [-]

,C P

[-]

[-]

0.6 0.8 1 1.2 1.40

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

Figure 4.1: Performance XPROP propeller, BEMT results. Black line indicates CT , red lineindicates CP the vertical axis for both of these line is shown on the left. The blue line indicates and its axis is shown on the right of the graph

J the values of CT and CP increase as would be expected. The maximum efficiency of thepropeller, at a blade pitch angle 0.7R = 30 [o], is around an advance ratio of 1.1, with a valueof approximately 0.81. At the lowest simulated advance ratio, J = 0.60, the value of CP isnearing its maximum, while for the CT value this is not yet the case.

The radial distributions of the lift and drag are shown in figures 4.42 to A.43 in section 4.3where it is compared to the results from the RANS analysis.

4.2 Results for the Reynolds-Averaged Navier-Stokes Equa-tions

Following the computations of the propeller performance using BEMT, this section will showthe results obtained using RANS simulations. RANS computes the values of aerodynamicproperties in volume cells surrounding the propeller blade. Because of this, more informationis known about the flow surrounding the blade as compared to the BEMT analysis. TheRANS analysis was executed using two different models. The first model, in which the flowis assumed to be fully turbulent, is discussed in section 4.2.1. The simulation in which thelaminar-turbulent transition is modeled using a correlation based model is treated in section4.2.2.


4.2 Results for the Reynolds-Averaged Navier-Stokes Equations 35

4.2.1 Turbulent Model Results

The fully turbulent simulations are obtained using the Spalart-Allmaras one-equation turbu-lence model, explained in section 2.3. As this model assumes the flow to be turbulent it isexpected there is a modeling error because of the exclusion of laminar flow.

To see if the solution of the simulation has converged enough, figure 4.2 shows the convergencehistory of the six turbulent simulations.

Iteration

De

ns

ity R

es

idu

al

0 5000 10000 15000 20000 25000

10-6

10-5

10-4

10-3

10-2

10-1

100J = 1.20J = 1.00J = 0.80J = 0.65J = 0.50J = 0.30

Figure 4.2: Simulation history of the density residual for the turbulent simulation

The convergence of the solution is checked by looking at the residual of the density, whichshould go to zero. After 25000 iterations it can be seen that all residuals are in the range of1e5, which is the range in which the solution is accepted as being converged. The simulationsstill show some oscillatory behaviour, but are accepted as they stay within the range of 1e5.

Figure 4.3 shows the Cp distribution on the suction side of the propeller for the investigatedadvance ratios. On the rotating propeller the Cp is defined as:

Cp =p p

12

(v2 + (2pinr)

2) (4.1)

As the advance ratio is decreased it can be seen that the pressure coefficient distributionchanges. At an advance ratio of J = 1.20 it can be seen that the pressure coefficient staysnear zero and is almost constant, as every change in color is a Cp difference of 1. Decreasingthe advance ratio one can see that the leading edge suction peak increases, both in strengthand size. As expected the suction peak is the largest and strongest near the tip of the blade,where the velocities are highest. To clarify the results a slice is investigated at rR = 0.7, shown



(a) J = 0.30 (b) J = 0.50 (c) J = 0.65

(d) J = 0.80 (e) J = 1.00 (f) J = 1.20

Figure 4.3: Cp distributions suction side propeller blade for the fully turbulent simulations, solidblack lines indicating rR = 0.7



in figure 4.4. In appendix A.1 additional results are shown for the slices at rR of 0.3, 0.4, 0.5,0.6, 0.8 and 0.9.

X/c [-]

C p [-]

0 0.2 0.4 0.6 0.8 1

-3

-2

-1

0

1

J = 0.30J = 0.50J = 0.65J = 0.80J = 1.00J = 1.20

Figure 4.4: Cp distributions atrR = 0.7 for the turbulent simulations

To investigate the boundary layer in more detail, figures 4.5 to 4.10 show the skin frictioncoefficient distributions over the suction side of the blade, where the skin friction coefficientis given as [4]:

Cf =2U2

(4.2)

Figure 4.5 shows the distributions for J = 1.20. Figure 4.5a shows the distribution of theabsolute value of the skin friction, |Cf |. It can be seen that the highest skin friction is in thestagnation point region. If looking at the components of the skin friction, given in figures4.5b to 4.5d, it can be seen that the value of the skin friction coefficient is dominated by theZ-component. This means that near the surface of the blade most of the flow is directed inthe positive Z-direction, as Cf,z is everywhere positive.

The advance ratio of 1.00 is given in figure 4.6 and this shows the same trend as for J = 1.20.The skin friction coefficient is dominated by the z-component. In comparison to J = 1.20 itcan be seen that at a lower advance ratio the value of |Cf | increases on the outward part ofthe blade. This is due to the increasing flow velocity at increasing radial position along theblade. While in the hub region of the blade the skin friction coefficient is comparable. Thissame trend can be seen for decreasing advance ratio down to J = 0.50. Comparing figures4.7, 4.8 and 4.9 it can be seen that the absolute skin friction coefficient is almost completelydescribed by the Z-component.



(a) |Cf | (b) Cf,x (c) Cf,y (d) Cf,zFigure 4.5: Absolute value of the skin friction coefficient and a breakdown of the skin frictioncoefficient in the three axial directions at J = 1.20





At J = 0.30, figure 4.10, it can be seen that the distribution of |Cf | shows a different patterncompared to the higher advance ratio values. Looking at the individual components it canbe seen that near the tip is a big region of reversed flow when looking at the X- and Z-components, see figures 4.10b and 4.10d. It is thought this is caused by the tip vortex createdby the preceding blade. To visualise the tip vortex, an isosurface plot of the absolute value ofthe vorticity, ||, is created, see figure 4.11. Figure 4.11a shows the tip vortex at J = 0.65.Here it can be seen that the vortex is not interfering with the blade. At J = 0.30 it can beseen that the tip vortex is very close to the blade surface, see figure 4.11b. Because the tipvortex is very close to the blade surface it can be expected that regions of reversed flow areforming on the blade surface as the ones which can be seen in figure 4.10.

Again a slice is made at rR = 0.7, and the skin friction coefficient on the suction side of theblade is compared, shown in figure 4.12. In figure 4.12a all investigated advance ratios can beseen. J = 0.30 shows a large value of Cf at the leading edge, after which it drops quickly tozero at an Xc of around 0.11. From here on a region of negative Cf is present. From

Xc = 0.375

to about Xc = 0.64 a region of positive skin friction can be seen. AfterXc = 0.64 a trailing

edge separation bubble can be seen. The advance ratio of J = 0.50 shows a short trailing edgeseparation bubble in the last 3% of the chord. The rest of the investigated advance ratiosdo not show the regions of negative Cf as could be seen from the figures 4.5 to 4.9. Fromfigure 4.12b it can be seen that a region of almost constant Cf can be seen after the firststeep decline, between Xc = 0.2 and 0.3, after which the Cf continues a slow decline towardthe trailing edge.




The boundary layer over the blade surface is further investigated by looking at the shapefactor, H, given in equation (1.4). To simplify this analysis only a 2-dimensional slice isinvestigated, as it is difficult to investigate this in 3 dimensions. To calculate H the flow fieldvariables perpendicular to the blade surface are extracted. The boundary layer height, 99, isestimated as the position where the parallel velocity is at its maximum. There is a maximumvelocity because there is a positive pressure gradient present in the direction perpendicularto the blade surface because of the blade curvature. This means the velocity decreases withincreasing distance to the surface. After the boundary layer height is determined the valuesfor the displacement thickness, , and the momentum thickness, , are calculated usingequations (1.2) and (1.3). Finally the shape factor can be calculated using the calculated and . The results for rR = 0.7 for the turbulent simulations can be seen in figure 4.13.The results are only shown for Xc > 0.1 as in the beginning there is a big influence from thestagnation point on the calculated results. In figure 4.13a all advance ratios can be seen. ForJ = 0.30 it can be seen there is immediately a peak in the shape factor, indicating separation.After the initial peak, the value of H drops to about 2.1. Following this the value of Hsteadily increases again to another peak near the trailing edge of the blade, again indicatinga region of separated flow.

Figure 4.13b shows the shape factor for the other advance ratios. These values all stay allstay below 2, except for J = 0.50 at the trailing edge showing an increase in H to about 2.15,which could explain the separation at the trailing edge.

Every iteration the DLR TAU code calculates the forces and moments in all directions. From



(a) J = 0.65

(b) J = 0.30

Figure 4.11: Vorticity isosurface plot, || = 1000, of the turbulent simulations at two differentadvance ratios with CP overlay



X/c [-]

C f [-]

0 0.2 0.4 0.6 0.8 1-2

-1.5

-1

-0.5

0

0.5

1

J = 0.30J = 0.50J = 0.65J = 0.80J = 1.00J = 1.20

(a)

X/c [-]

C f [-]

0 0.2 0.4 0.6 0.8 1-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

J = 0.65J = 0.80J = 1.00J = 1.20

(b)

Figure 4.12: Cf distributions of the blade suction side atrR = 0.7 for the turbulent simulations,

(a) showing the full range of simulated advance ratios and (b) range without J = 0.30 and 0.50



X/c [-]

H [-]

0 0.2 0.4 0.6 0.8 1

1.5

2

2.5

3

3.5

4

4.5

5

J = 0.30J = 0.50J = 0.65J = 0.80J = 1.00J = 1.20

(a)

X/c [-]

H [-]

0 0.2 0.4 0.6 0.8 11.4

1.6

1.8

2

2.2

2.4

J = 0.50J = 0.65J = 0.80J = 1.00J = 1.20

(b)

Figure 4.13: Shape factor H for the blade suction side at rR = 0.7 for the turbulent simulation,(a) full range of investigated advance ratios and (b) range without J = 0.30



Table 4.2: Results obtained using the turbulent RANS model

J [-] CT [-] CP [-] [-]1.20 0.1115 0.1713 0.78131.00 0.1893 0.2482 0.76270.80 0.2597 0.3018 0.68850.65 0.3084 0.3294 0.60840.50 0.3553 0.3508 0.50630.30 0.3962 0.4021 0.2956

these forces and moments the thrust, T , and torque, Q, can be calculated, which can be usedto determine the performance of the XPROP propeller. The performance results calculatedfrom the fully turbulent simulations are given in table 4.2 and are shown in figure 4.14.

J [-]

C T [-]

,C P

[-]

[-]

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.20

0.1

0.2

0.3

0.4

0.5

0.6

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

Figure 4.14: Performance XPROP propeller, turbulent RANS results. Black line indicates CT ,red line indicates CP the vertical axis for both of these line is shown on the left. The blue lineindicates and its vertical axis is shown on the right of the graph

From the results of the fully turbulent performance values, given in table 4.2 and figure 4.14,it can be seen that for decreasing J the values of CT and CP are increasing. It is expectedthat at low advance ratios, the values of CT and CP would start decreasing. However, inthe case of CP the opposite can be seen, at low advance ratios the value CP increases. It isthought this is due to the tip vortex of the preceding blade passing close to the blade surface.Because of this regions of reversed flow are forming on the blade surface, which increases thedrag of the propeller and thus increasing the power needed. The efficiency of the propellerincreases for increasing J , where it can be seen that at J = 1.20, is almost at its maximum.



4.2.2 Transition Model Results

Using the transition model developed by Langtry and Menter [34], the flow field around theXPROP propeller is calculated. The model is explained in more detail in section 2.3. Due tothe inclusion of laminar-turbulent transition it is hoped that this model is able to predict theperformance of the XPROP propeller more accurately compared to the simulations withoutlaminar-turbulent transition.

The history of the density residual is checked to see if all simulations are converged, thesecan be seen in figure 4.15. As is the case with the turbulent simulations 25000 iterations aretaken to see if the solution is converged. Two simulations show density residuals which are inthe range of 1e3. The J = 0.30 simulation does not reach density residual values far below1e3 whereas the simulation for J = 0.50 appears to converge for the first 16000 iterationsafter which it quickly jumps to a density residual of approximately 2e3. From this it canbe concluded that the results from the J = 0.30 and J = 0.50 cases are not to be trusted.Because no intermediate solutions are available, it is not known what caused the solutions tonot converge.

Iteration

De

ns

ity R

es

idu

al

0 5000 10000 15000 20000 25000

10-5

10-4

10-3

10-2

10-1

100J = 1.20J = 1.00J = 0.80J = 0.65J = 0.50J = 0.30

Figure 4.15: Simulation history of the density residual for the transition simulation

In figures 4.16a to 4.16f the Cp distributions on the suction side of the propeller blade areshown for all simulated advance ratios, including the two cases which were not fully converged.The simulation for the case of J = 1.20, given in figure 4.16f, shows only small differencesin pressure coefficient compared to the other simulations. From an advance ratio of J =1.00 strange structures start occurring on the blade surface which increase in strength withdecreasing advance ratio, until no clear structures can be distinguished at an advance ratio ofJ = 0.50. Figure 4.17 shows the Cp values on the blade surface at rR = 0.7. For J = 0.3 threebumps can be seen in the Cp distribution on the suction side. One can see that for J = 0.65



(a) J = 0.30 (b) J = 0.50 (c) J = 0.65

(d) J = 0.80 (e) J = 1.00 (f) J = 1.20

Figure 4.16: Cp distributions suction side propeller blade for the transition simulations



two peaks can be seen on the suction side, at Xc = 0.3 andXc = 0.475. At higher advance

ratios these peaks are no longer clearly visible. In appendix A.1 additional results are shownfor the slices at rR of 0.3, 0.4, 0.5, 0.6, 0.8 and 0.9.

X/c [-]

C p [-]

0 0.2 0.4 0.6 0.8 1

-3

-2

-1

0

1

J = 0.30J = 0.50J = 0.65J = 0.80J = 1.00J = 1.20

Figure 4.17: Cp distributions atrR = 0.7 for the transition simulations

It is thought that the peaks occuring in the Cp distribution on the blade surface are causedby the strange structures starting to form at J = 1.00. To see what causes these strangestructures, first the Cf distribution on the propeller surface is investigated. Figure 4.18ashows the value of Cf on the suction side of the propeller, where a solid line at rR = 0.5 isshown as a slice is extracted from the domain at this location which is used to investigate theflowfield surrounding the propeller blade.

Figure 4.18b focusses more at the region surrounding rR = 0.5, here the strange structurescan be seen more clearly. In figure 4.18b the skin friction direction is visualised, this is doneto see the direction of the flow just above the surface. At the leading edge of the blade it canbe seen that the flow has only a small component in the Y -direction. After a short distanceit can be seen that the flow is directed more and more in positive Y -direction, this meansthat both the X- and Z-component of the skin friction are becoming smaller. At around 40%chord it can be seen that the flow is directed completely in the positive Y -direction, meaningthat both the X- and Z-component approach zero, indicating the start of flow separation.After a while the strange structures are forming on the blade surface. Looking at the flowtopology of one of the strange structures it looks as though some sort is vortex is formed. Toinvestigate this in more detail, a slice is extracted at rR = 0.5.

Figure 4.19 shows the Cp values in the neighbourhood of the propeller blade together withsome flow streamlines, only the X- and Z-components of the velocity are used. At the aft partof the blade it can be seen that a second low pressure area is forming, see figures 4.19a 4.19b.



(a) (b)

Figure 4.18: Skin friction coefficient, Cf , distribution on the suction side of the propeller bladeat J = 1.00, (a) full propeller blade, solid line indicating rR = 0.5 and (b) focus around

rR = 0.5

where both Cf and the skin friction direction is visualised



(a)

(b)

Figure 4.19: Cp distribution, J = 1.00, in the flowfield surrounding the propeller blade includingstreamtraces at rR = 0.5, (a) full blade section and (b) aft part of the blade section



Looking at the streamlines at this location it can be seen a rather large separation bubble isforming. The flow above the separation bubble is accelarated and thus creating the secondlow pressure area. In figure 4.19b it can be seen that a smaller separation bubble already waspresent upstream of the large separation bubble, which is originating from another vortexstructure, see figure 4.19b.

To see where the vortices are originating from, the value of the intermittence, , is investigated,see figure 4.20. The value of varies between 0 and 1, where 0 means laminar flow and 1 isturbulent flow. Looking at figure 4.20a it can be seen that in the farfield the value of is 1and near the propeller blade it decreases to 0. When zooming in on the trailing edge of thepropeller blade, see figure 4.20b, it can be seen that the value of decreases to 0 at the wall,even at the location where turbulent flow is expected. From the description of the transitionmodel [34] it is known that the boundary condition for at a wall is a zero normal flux, soa Neumann boundary condition. But when looking at figure 4.20b it looks like a Dirichletboundary condition is implemented in the TAU code. It is thought that because of this thevortex like structures are forming over the propeller blade surface at lower advance ratios.

The skin friction coefficient is investigated on the suction side of the blade, as shown in figures4.21 to 4.25. Figure 4.21a shows |Cf | for J = 1.20. Here a region of low skin friction can beseen at around the halfway chord. Looking at the single components of Cf , it can be seen thatafter the low skin friction region, a region of negative Cf,x and Cf,z is shown. Also it can beseen that Cf,y has a big influence on the absolute skin friction value, indication flow directedtoward the blade tip. Combining this leads to the conclusion that at J = 1.20 trailing edgeseparation occurs.

Decreasing the advance ratio to 1.00, see figure 4.22, one can also see the vortical structuresforming as could be seen in the Cp distributions. Looking at the three components, one cansee a separation line, indicated by the purple regions at 13 to

12 chord in Cf,x and Cf,z. The

structures consist of both positive and negative values of Cf,x and Cf,z, indicating a vortexlike structure, while having a mostly positive value of Cf,y, which means that the flow againis directed toward the blade tip.

At J = 0.80, the strength of the vortex like structures is increasing as can be seen by theincrease in the value of the skin friction. Looking at the Cf,x and Cf,z components, it lookslike the vortex like structures start to form a strong separation line, right behind a separationline which is weaker, indicated by the blue/purple colour. This is an indication that the flowseparates, has a short reattachment and then separates again, creating a bigger separationbubble. The Cf,y component shows a strong flow direction toward the tip of the blade afterthe flow starts to separate, see figures 4.23c and 4.23d. Another thing of interest is the shapeof the separation line. Where at J = 1.20 and J = 1.00 the separation line is relativelystraight, starting from J = 0.80 it can be seen that at the outward portion of the blade theseparation is postponed until approximately half chord, while in the middle part of the bladeseparation starts to occur near the leading edge.

Figure 4.24 shows the breakdown of the skin friction coefficient in its three components forJ = 0.65. Comparing J = 0.80 to J = 0.65, one can see the same structure occurring. Butthe differences being a stronger separation, the region where leading edge separation occurs



(a)

(b)

Figure 4.20: Distribution of the intermittency, , in the surrounding flowfield, at J = 1.00, ofthe propeller blade at rR = 0.5, (a) full blade section and (b) focus on the trailing edge part ofthe blade section




moves upward to the tip and the flow structure at the tip is changing.

Looking at the Cf distributions for J = 0.50 and J = 0.30, shown in figures 4.25a and 4.25b,it is difficult to make out what happens. For J = 0.50 it looks as if the separation line hasbursted, giving rise to the failure in convergence.

At J = 0.30 it looks as if the same problem is occurring as with the turbulent RANS simu-lation, the interaction of the tip vortex of a preceding blade with the flow over the surface,this can be seen in more detail in figure 4.26. Figure 4.26a shows an isosurface plot of theabsolute vorticity value at J = 0.65, while figure 4.26b shows the isosurface plot at J = 0.30.Comparing the two figures it can be seen that, at the low advance ratio, the tip vortex is verynear to the surface of the blade and it is possible this has an effect on the flow, as was thecase with the simulations using the Spalart-Allmaras model from section 4.2.1.

When a slice is analysed at rR = 0.7, see figure 4.27, one can see that at J = 0.30 and J = 0.50Cf values are out of range compared to the other simulations. In figure 4.27b J = 0.30 andJ = 0.50 are removed. In this figure it can be seen that at rR = 0.7 the flow for J = 0.65separates early, at Xc = 0.18, but it reattaches again at

Xc = 0.55, after which the flow stays

attached up to Xc = 0.96. The flow at J = 0.80 separates atXc = 0.46 and reattaches again

at Xc = 0.92. Where the flows for J = 0.65 and J = 0.80 reattach, at J = 1.00 and J = 1.20no reattachment of the flow occurs. J = 1.00 flow separates at Xc = 0.575, and for J = 1.20flow separates at Xc = 0.66. It can be seen from this, decreasing the advance ratio, decreasesthe separation position. But early separation leads to reattachment of the flow, as is the case


4.2 Results for the Reynolds-Averaged Navier-Stokes Equa

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